caa a22 4500 465751709 CHVBK 20180323111835.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF02238798 doi (NATIONALLICENCE)springer-10.1007/BF02238798 Chan R. Department of Mathematics and Statistics, University of Auckland, Private Bag, Auckland, New Zealand aut On symmetric Runge-Kutta methods of high order [Elektronische Daten] [R. Chan] Symmetrische Runge-Kutta Methoden höherer Ordnung The usual characterization of symmetry for Runge-Kutta methods is that given by Stetter. In this paper an equivalent characterization of symmetry based on theW-transformation of Hairer and Wanner is proposed. Using this characterization it is simple to show symmetry for some well-known classes of high order Runge-Kutta methods which are based on quadrature formulae. It can also be used to construct a one-parameter family of symmetric and algebraically stable Runge-Kutta methods based on Lobatto quadrature. Methods constructed in this way and presented in this paper extend the known class of implicit Runge-Kutta methods of high order. Springer-Verlag, 1990 Symmetry nationallicence Algebraic stability nationallicence Lobatto nationallicence Computing Springer-Verlag 45/4(1990-12-01), 301-309 0010-485X 45:4<301 1990 45 607 https://doi.org/10.1007/BF02238798 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02238798 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Chan R. Department of Mathematics and Statistics, University of Auckland, Private Bag, Auckland, New Zealand aut NATIONALLICENCE 773 0- Computing Springer-Verlag 45/4(1990-12-01), 301-309 0010-485X 45:4<301 1990 45 607 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer